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Exchangeability type properties of asset prices

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  • Ilya Molchanov
  • Michael Schmutz
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    Abstract

    In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call symmetry property and the duality principle in option pricing. A particular attention is devoted to the case of asset prices driven by Levy processes. Based on this, concrete semi-static hedging techniques for multi-asset barrier options, such as certain weighted barrier spread options, weighted barrier swap options or weighted barrier quanto-swap options are suggested.

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    File URL: http://arxiv.org/pdf/0901.4914
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0901.4914.

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    Date of creation: Jan 2009
    Date of revision: Apr 2011
    Handle: RePEc:arx:papers:0901.4914

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    Web page: http://arxiv.org/

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    1. José Fajardo & Ernesto Mordecki, 2006. "Pricing Derivatives On Two-Dimensional Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 185-197.
    2. Ernst Eberlein & Antonis Papapantoleon & Albert N. Shiryaev, 2008. "Esscher transform and the duality principle for multidimensional semimartingales," Papers 0809.0301, arXiv.org, revised Nov 2009.
    3. José Fajardo & Ernesto Mordecki, 2005. "Duality and Derivative Pricing with Time-Changed Lévy Processes," IBMEC RJ Economics Discussion Papers 2005-12, Economics Research Group, IBMEC Business School - Rio de Janeiro.
    4. Michael Schmutz, 2008. "Semi-static hedging for certain Margrabe type options with barriers," Papers 0810.5146, arXiv.org, revised Feb 2010.
    5. Laurence, Peter & Wang, Tai-Ho, 2009. "Sharp distribution free lower bounds for spread options and the corresponding optimal subreplicating portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 35-47, February.
    6. JosE Fajardo & Ernesto Mordecki, 2006. "Symmetry and duality in Levy markets," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 219-227.
    7. Ernst Eberlein & Antonis Papapantoleon & Albert Shiryaev, 2008. "On the duality principle in option pricing: semimartingale setting," Finance and Stochastics, Springer, vol. 12(2), pages 265-292, April.
    8. José Fajardo & Ernesto Mordecki, 2006. "Skewness Premium with Lévy Processes," IBMEC RJ Economics Discussion Papers 2006-04, Economics Research Group, IBMEC Business School - Rio de Janeiro.
    9. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February.
    10. José Fajardo & Ernesto Mordecki, 2008. "Symmetry and Time Changed Brownian Motions," IBMEC RJ Economics Discussion Papers 2008-02, Economics Research Group, IBMEC Business School - Rio de Janeiro.
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    Cited by:
    1. Rheinländer, Thorsten & Schmutz, Michael, 2013. "Self-dual continuous processes," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1765-1779.
    2. Ilga Molchanov & Michael Schmutz & Kaspar Stucki, 2012. "Invariance properties of random vectors and stochastic processes based on the zonoid concept," Statistics and Econometrics Working Papers ws122014, Universidad Carlos III, Departamento de Estadística y Econometría.

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